My laptop won't boot Natty beta 2 unless it is plugged in most of the time (like 2 out of 3 times). After it is booted I am able to unplug it and let it run on battery power with no problems. Sometimes I will be able to boot on just battery power, other times it will hang at either a blank, purple screen right after grub2 or at the flashing "_" screen.

Another interesting thing is that it will only have this problem on the new 2.6.38-8 linux kernel, natty will boot normally on the 2.6.35-22 kernel (i have both because it was an upgrade from 10.10.
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user14274Apr 14 '11 at 20:27

It appears that the latest kernel update (2.6.38-10-generic) has fixed the issue on the Y560. In the bug report posted above it does seem that some people are still having issues with other things but you may try and see if it works.
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user16286Jul 16 '11 at 3:18